Basic relation between numerical range and Davis-Wielandt shell of an operator $A$ acting on a Hilbert space with orthonormal basis $xi={e_{i}|i in I}$ and its conjugate $bar{A}$ which is introduced in this paper are obtained. The results are used to study the relation between point spectrum, approximate spectrum and residual spectrum of $A$ and $bar{A}$. A necessary and sufficient condition fo...

A natural generalization of analytic functions to n-dimensional Euclidean space are quasiregular mappings.(See [2] and [3].) An analogue of Theorem 1.1 for quasiregular mappings in John domains in Euclidean space appeared in [4]. Recently the analytical tools used in the proof of this result have been generalized to Carnot groups. We give an account of some of these advances and obtain an analo...

We consider a sequence HN of finite-dimensional Hilbert spaces of dimensions dN → ∞. Motivating examples are eigenspaces, or spaces of quasi-modes, for a Laplace or Schrödinger operator on a compact Riemannian manifold. The set of Hermitian orthonormal bases of HN may be identified with U(dN), and a random orthonormal basis of is a choice of a random sequence UN∈U(dN) from the product of normal...

A provably stable reduced order model, based on a projection onto a scaled orthonormal Laguerre basis, followed by a SVD step, is proposed. The method relies on the conformal mapping properties induced by the complete orthonormal scaled Laguerre basis, allowing a mapping from the discrete-stable case to the continuous-stable case and vice versa.

In this paper we show the finite dimensionality of real linear spaces with their carriers equal R n. We also give the standard basis of such spaces. For the set R n we introduce the concepts of linear manifold subsets and orthogonal subsets. The cardinality of orthonormal basis of discussed spaces is proved to equal n. We use the following convention: i, j, n are elements of N, z, B 0 are sets,...

We describe QCH Kähler surfaces $(M,g,J)$ of generalized orthotoric type. introduce a distinguished orthonormal frame on $(M,g)$ and give the structure equations for $(M,g,J)$. In case when opposite Hermitian $I$ is conformally